Regularized inversion of full tensor magnetic gradient data

Authors

DOI:

https://doi.org/10.26089/NumMet.v17r103

Keywords:

magnetostatics, full tensor magnetic gradient data, inverse problems, ill-posed problems, regularization method

Abstract

Features of numerical solution of the three-dimensional ill-posed problem devoted to the inversion of full tensor magnetic gradient data are considered. This problem is simulated by a system of two three-dimensional Fredholm integral equations of the first kind. The Tikhonov regularization is applied to solve this ill-posed problem. The conjugate gradient method is used as a minimization method. The choice of the regularization parameter is realized according to the generalized residual principle with consideration of round-off errors capable of affecting the final result of calculations significantly.

Author Biographies

Y. Wang

Institute of Geology and Geophysics, Chinese Academy of Sciences
Beitucheng Western Road, 19, 100029, Beijing, China
• Professor

D.V. Lukyanenko

A.G. Yagola

References

  1. Vl. V. Voevodin, S. A. Zhumatii, S. I. Sobolev, et al., “Practice of ’Lomonosov’ Supercomputer,” Otkrytye Sistemy, No. 7, 36-39 (2012).
  2. P. G. Leliévre and D. W. Oldenburg, “Magnetic Forward Modelling and Inversion for High Susceptibility,” Geophys J. Int. 166 (1), 76-90 (2006).
  3. Y. Li and D. W. Oldenburg, “3-D Inversion of Magnetic Data,” Geophysics 61 (2), 394-408 (1996).
  4. A. Pignatelli, I. Nicolosi, and M. Chiappini, “An Alternative 3D Inversion Method for Magnetic Anomalies with Depth Resolution,” Ann. Geophys. 49 (4/5), 1021-1027 (2006).
  5. D. V. Lukyanenko, A. G. Yagola, and N. A. Evdokimova, “Application of Inversion Methods in Solving Ill-Posed Problems for Magnetic Parameter Identification of Steel Hull Vessel,” J. Inverse Ill-Posed Probl. 18 (9), 1013-1029 (2011).
  6. D. V. Lukyanenko and A. G. Yagola, “Application of Multiprocessor Systems for Solving Three-Dimensional Fredholm Integral Equations of the First Kind for Vector Functions,” Vychisl. Metody Programm. 11, 336-343 (2010).
  7. A. Christensen and S. Rajagopalan, “The Magnetic Vector and Gradient Tensor in Mineral and Oil Exploration,” Preview 84, 77 (2000).
  8. P. Heath, G. Heinson, and S. Greenhalgh, “Some Comments on Potential Field Tensor Data,” Explor. Geophys. 34 (2), 57-62 (2003).
  9. M. Schiffler, M. Queitsch, R. Stolz, et al., “Calibration of SQUID Vector Magnetometers in Full Tensor Gradiometry Systems,” Geophys. J. Int. 198 (2), 954-964 (2014).
  10. P. W. Schmidt and D. A. Clark, “Advantages of Measuring the Magnetic Gradient Tensor,” Preview 85, 26-30 (2000).
  11. P. Schmidt, D. Clark, K. Leslie, et al., “GETMAG - a SQUID Magnetic Tensor Gradiometer for Mineral and Oil Exploration,” Explor. Geophys. 35 (4), 297-305 (2004).
  12. M. S. Zhdanov, H. Cai, and G. A. Wilson, “3D Inversion of SQUID Magnetic Tensor Data,” J. Geol. Geosci. 1, 1-5 (2012).
  13. S. Ji, Y. Wang, and A. Zou, “Regularizing Inversion of Susceptibility with Projection onto Convex Set Using Full Tensor Magnetic Gradient Data,” Inverse Probl. Sci. Eng. 2016 (in press).
  14. V. A. Morozov, “Regularization of Incorrectly Posed Problems and the Choice of Regularization Parameter,” Zh. Vychisl. Mat. Mat. Fiz. 6 (1), 170-175 (1966) [USSR Comput. Math. Math. Phys. 6 (1), 242-251 (1966)].
  15. A. N. Tikhonov, A. V. Goncharskii, V. V. Stepanov, and A. G. Yagola, Numerical Methods for Solving Incorrect Problems (Nauka, Moscow, 1990) [in Russian].
  16. N. N. Kalitkin and L. V. Kuz’mina, “Improved Form of the Conjugate Gradient Method,” Mat. Model. 23 (7), 33-51 (2011) [Math. Models Comput. Simul. 4 (1), 68-81 (2012)].
  17. N. N. Kalitkin and L. V. Kuz’mina, “Improved Forms of Iterative Methods for Systems of Linear Algebraic Equations,” Dokl. Akad. Nauk 451 (3), 264-270 (2013) [Dokl. Math. 88 (1), 489-494 (2013)].

Published

2016-02-02

How to Cite

Ван Я., Лукьяненко Д.В., Ягола А.Г. Regularized Inversion of Full Tensor Magnetic Gradient Data // Numerical methods and programming. 2016. 17. 13-20. doi 10.26089/NumMet.v17r103

Issue

Section

Section 1. Numerical methods and applications

Most read articles by the same author(s)

1 2 3 > >>